Some of the most prized violins in the world were crafted in the Italian workshops of Amati, Stradivari, and Guarneri — master violinmaking families from the 17th and 18th centuries who produced increasingly powerful instruments in the renaissance and baroque musical eras. These violins, worth millions of dollars today, represent the Cremonese period — what is now considered the golden age of violinmaking.

Now acousticians and fluid dynamicists at MIT, along with violinmakers at the North Bennet Street School in Boston, have analyzed measurements from hundreds of Cremonese-era violins, identifying key design features that contribute to these particular violins’ acoustic power, or fullness of sound.

The team acquired technical drawings of Cremonese-era violins from museums, collector databases, and books, as well as X-ray and CAT scans of the instruments. They compared the dimensions of various features from one instrument to another, as well as measurements of acoustic resonances across instruments.

The researchers found that a key feature affecting a violin’s sound is the shape and length of its “f-holes,” the f-shaped openings through which air escapes: The more elongated these are, the more sound a violin can produce. What’s more, an elongated sound hole takes up little space on the violin, while still producing a full sound — a design that the researchers found to be more power-efficient than the rounder sound holes of the violin’s ancestors, such as medieval fiddles, lyres, and rebecs.

The thickness of a violin’s back plate also contributes to its acoustic power. Violins carved from wood are relatively elastic: As the instrument produces sound, the violin’s body may respond to the air vibrations, contracting and expanding minutely. A thicker back plate, they found, would boost a violin’s sound.

The researchers found that as violins were crafted first by Amati, then Stradivari, and finally Guarneri, they slowly evolved to more elongated f-holes and thicker back plates.

But were the design changes intentional? To answer this question, the researchers worked the measurements from hundreds of Cremonese-era violins into an evolutionary model, and found that any change in design could reasonably be explained by natural mutation — or, in this case, craftsmanship error.

In other words, makers may have crafted violins with longer sound holes and thicker back plates not by design, but by accident.

“We found that if you try to replicate a sound hole exactly from the last one you made, you’ll always have a little error,” says Nicholas Makris, a professor of mechanical and ocean engineering at MIT. “You’re cutting with a knife into thin wood and you can’t get it perfectly, and the error we report is about 2 percent … always within what would have happened if it was an evolutionary change, accidentally from random fluctuations.”

Makris stresses that while each violinmaker inarguably possessed a good ear — in order to recognize and replicate the violins that sounded best — whether they recognized the particular design elements that contribute to a more powerful sound is still up for debate.

“People had to be listening, and had to be picking things that were more efficient, and were making good selection of what instrument to replicate,” Makris says. “Whether they understood, ‘Oh, we need to make [the sound hole] more slender,’ we can’t say. But they definitely knew what was a better instrument to replicate.”

Makris and his colleagues from MIT and the North Bennett Street School publish their results this week in the Proceedings of the Royal Society: A.

There’s power in shape

Makris didn’t originally set out to study violin acoustics: His work is primarily in ocean exploration with acoustics, developing and applying technology to sense marine life and ocean phenomenon over large areas. But about a decade ago, he took up a new hobby, playing the lute.

“I’m an acoustics expert, but promised myself I wouldn’t think about the acoustics of the instrument, I’m just going to play the thing,” Makris remembers.

That thinking didn’t last long, as Makris started talking with lutemakers and players in an effort to better understand the instrument — which was once Europe’s most popular, but became effectively extinct for centuries before its recent re-emergence. The lute is much quieter than the violin: In addition to other design differences, its sound holes are circular rather than f-shaped, with elaborate interior carvings known as rosettes, inherited from the lute’s Middle Eastern ancestor, the oud.

Several years ago, a noted lute player approached Makris with an intriguing quandary: Do the carvings within a lute’s sound hole make a difference to the overall sound produced? Makris realized that the relevant frequencies of sound were in the range where airflow through the sound hole behaves nearly as an incompressible fluid, and enlisted the help of Yuming Liu, a principal research scientist in MIT’s Department of Mechanical Engineering.

The team modeled the airflow through a simple round hole, as well as a more elaborately patterned hole of the same diameter, and found that in both cases, the air flowed fastest at the hole’s periphery; its interior, whether open or partially filled, did not significantly affect the airflow. 

Answering the musician’s simple question turned into a seven-year project in which the team examined the acoustic dynamics of stringed instruments through time, from the oud, lute, and medieval fiddles to the guitar and ultimately the violin — a period spanning from the 10th century to the 18th century. Analysis of the violin came at the urging of team member Roman Barnas, director of violinmaking and repair at the North Bennet Street School, an expert on the construction of early instruments.

Throughout the 800-year period the researchers examined, they noted an evolution in sound-hole shape — from a simple round hole to a semicircle, which eventually morphed into a c-shape that grew more elongated, ultimately assuming the f-shape of the violin. The perimeter of these shapes steadily grew, while the area of the interior void gradually decreased.

As with the evolution in length of the violin’s f-hole during the Cremonese period, Makris’ team found that the overall shape of the violin’s ancestors slowly evolved to be more powerful and more acoustically efficient — though not necessarily by design.

“We think these changes are still within the possibility of natural mutation,” Makris says. “All of these subtle parameters of shape, we’ve modeled, and are able to make very good predictions on what the effects will be on frequency and power.”

Makris says the group’s results may be useful for master violinmakers looking to design more powerful, fuller-sounding instruments — although he acknowledges that there’s more to producing a quality violin than adjusting a few parameters.

“Mystery is good, and there’s magic in violinmaking,” Makris says. “Some makers, I don’t know how they do it — it’s an art form. They have their techniques and methods. But here, for us, it’s good to understand scientifically as much as you can.”

This research was funded in part by the Office of Naval Research.

What proportion of the sound comes from the top?Is this about sound coming "out" of the hole, or the effect of the hole shape on the top?Is this only about volume, or also sound quality?An interesting soundhole related article here:http://www.tejagerken.com/Arti...

For some 70 years I have been playing the violin and the viola as an amateur. My interest in the technology of violins was stimulated by a study in Scientific American long ago about creating a family of violins from small to very large. The acoustic studies were done with powder designs as the instrument was vibrated. This article provides a new concept -- evolution of non-living things!

The son (Steve Conner) of a close friend is an innovative master guitar maker. He started creating a hole directed up on the side of his guitars because, as also a player himself, he understood that players wanted to hear the sound really clearly. This is interesting in its own right. It also may answer in part some of Marilyn Hunter's questions. It says that sound, for a guitar, indeed comes out of the hole. It suggests that the holes may have a little to do with volume, but nothing to do with sound quality (except for the player).

Have they actually verified in how far the violins they were studying were actually containing wood stemming from the time the owners claim they were build? Otherwise the whole study says nothing about historical evolution at all. Most cremona school violins in use were most certainly often repaired to continue to be played. This is necessary for most violins ever few years. And every time smaller or larger bits of the instrument are repaired, replaced, etc. Image this proces continuïng for 3 - 4 centuries and one may truly ask the question which violin it is or has become over time. And so it may be very well that what your are seeing today is the outcome of that process and not a 17th of 18th original.

Interesting article. However, as is often the case with scientific research about musical instrument acoustics, perhaps insufficient attention is given to the negative factors inherent in any design change. More careful consideration of the holistic effects caused by specific changes could lead to research focused on their pivotal nature. Questions must be raised as to what other changes may need to occur to compensate for the sometimes inevitable effects of new developments.

About 3 to 4 decades ago, a science program (NOVA?) investigated how violins produced sound over so many different frequencies.

They identified at least four design elements that worked like 4-way high fidelity speakers (base, mid-range, tweeter, super-tweeter). The highest frequencies were played most efficiently by the bridge itself, the violin's super-tweeter. The next level of frequencies were most efficiently played from an up and down motion of the center of the top plate, between the contact points of the sound board (a stick that connects the front and back of the top, with a small curving gap between). The next level of frequencies were most efficiently played from a rocking motion of the top plate, made possible by the sound board. The lowest frequencies were most efficiently played from a bellows motion between the top and bottom plates.

And the bottom plate had another design trick: on the best violins, the base plate is thinner in the middle than the edges, and the thinning is asymmetrical. The asymmetrical thinning is associated with the traditional asymmetrical placement of a small dowel between the top and bottom plates, held in place by friction and the compression between the plates. The dowel and the asymmetric thinning makes the bellows action more efficient.

And the best violin designs are like the best 3-way and 4-way speakers: as power drops off for one design element at transition frequencies, the next design element begins to pick up, compensating for the power loss. Like properly tuned cross-over circuits in electronic 4-way speakers, the best crafted violins have an even distribution of sound levels across all frequencies.

A surprisingly sophisticated achievement for craftsmen who lived two to three centuries before scientists would be capable of measuring their craftsmanship in waveforms on oscilloscopes.

very interesting article. I don't know whether the writers follow this comment or not, but still I have few questions. 1) if the f-hole is so important to make the sound more powerful, why still guitarists have stuck to O-holes? yes, I admit that there are guitars also with f-holes but in general guitars are O-hole. why not classical guitarists are going for a f-hole? Does O-hole contain some other beauty? 2) doesn't the upper wood plate has some contribution to a good sound quality? does it all depend on the back wood plate? have you examined that also? there is no mention of that. 3) you have stated that if we increase the seize of the f-hole the sound get more powerful, but it should have some limit. isn't it? if it is not, then I can make a violin with f-holes as big as the body, then will it work? I don't think so.

Thank you, would like to hear more from you.

I haven't read all the comments, so this may be a repeated comment: The obvious follow up to the research would be to use science to design the very best amplification-hole design. Unless the F-hole as is, is truly the very best design in existence. I understand the "sound quality" may be subjective, but at least some notation on what shape of the hole and thickness/stiffness/material of the back plate gives the maximum amplification without changing the overall shape/size/sound of the instrument.

Very interesting article-- Readers (and the researchers) might be interested in the book, CREMONA VIOLINS. A PHYSICIST'S QUEST FOR THE SECRETS OF STRADIVARI, by Kameshwar C. Wali (my father!), published in 2010, by World Scientific. The book describes the research of physicist William F. "Jack" Fry, over several decades to understand the Stradivari sound and replicate it. Wali's book describes how Fry discovered an essential "secret" of the Stradivari method.

This is an interesting article; however, there is much more to it. Firstly, the fact that BOTH F holes are effectively symmetrical amuses me as one is bass responsive and the other is tenner responsive. Different modes of oscillation and air movement. I think as important as the F holes are, so are the features of the F holes and the surrounding "excavation" of material surrounding the boundary of the F holes, esp. the area on the outer edge of the instrument. There is a "fillet" between the edge and the F hole that effects the natural frequency and behavior of the material outlining the F hole. Also, one of the most notable features of an F hole are the tongues formed by or near the initial defining holes of the F holes.

I find it rather odd that this article says that everything that has made the Masters violins were accidentally found. Perhaps some characteristics may have been accidental, however a true tradesman always tries to find better ways in their trade continually throughout their lifetime. Science is good at proving things that you can examine,and hold physically, all the rest is speculation, and this is where science falls flat on its face.Im apt to believe that most that has been put into the modern violin was through purposeful trial and error.This however was an interesting article and interesting and valuable comments.

My research has been about violin structure and function. For me the F-hole is a slit that makes it possible to produce specific dynamic quality. The bout shapes move outward and part of the structure between the F-holes downward. This also means that we have two structure, thus bout shapes, that must be optimized to produce equal breathing condition. When this happens the F-hole is just the opening too let this happen. However, the F-hole is more a technical solution optimizing the dynamic function. Any hole in the structure, the rib, could be used to allow breathing but than the violin will not function as it does. www.zuger.se.

Does the research scale up to the viola, cello, and double bass?

F-holes have a higher proportion of perimeter compared to area than the circular hole of a guitar which has the lowest proportion that is possible.

An F-hole for an archtop guitar adds sparkle to the tone which can complement its use as a jazz instrument.

This article was obviously not written by a successful experienced violin maker. Some of the most powerful violins I have witnessed in my career of over 40 years as a maker have short f-holes modeled after Stradivari. Length of f hole is only one of many factors that all must work together to make a fine, powerful violin.

Reprinted with permission of MIT News